Continuous connection between the two record classes

Determine whether the Haldane and trivial record classes can be joined continuously, thereby establishing whether a record has phases in the full sense rather than only distinct classes.

Background

The paper constructs a transition between a Haldane-class record and a trivial-class record using symmetry-protected sectors with different bond representations. In the exhibited example, covariance prevents the sectors from mixing, so their leading transfer eigenvalues cross at a first-order transition where the fixed-point structure becomes nonunique.

It remains unresolved whether the two classes can instead be connected continuously in a suitable symmetry-preserving setting. The authors identify this question as bearing on whether records possess genuine phases or merely classifications into distinct classes.